Shapira Matrix-Based Multigrid

Theory and Applications
2. Auflage 2008
ISBN: 978-0-387-49765-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2, 341 Seiten, eBook

Reihe: Numerical Methods and Algorithms

Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems.

This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.

Zielgruppe

Research

Autoren/Hrsg.

Shapira, Yair

Inhaltsverzeichnis

List of Figures
List of Tables
Preface
Part I. Concepts and Preliminaries
1. The Multilevel–Multiscale Approach
2. Preliminaries
Part II. Partial Differential Equations and Their Discretization
3. Finite Differences and Volumes
4. Finite Elements
Part III. Numerical Solution of Large Sparse Linear Systems
5. Iterative Linear System Solvers
6. The Multigrid Iteration
Part IV. Multigrid for Structured Grids
7. Automatic Multigrid
8. Applications in Image Processing
9. Black-Box Multigrid
10. The Indefinite Helmholtz Equation
11. Matrix-Based Semicoarsening
Part V. Multigrid for Semi-Structured Grids
12. Multigrid for Locally Refined Meshes
13. Application to Semi-Structured Grids
Part VI. Multigrid for Unstructured Grids
14. Domain Decomposition
15. The Algebraic Multilevel Method
16. Applications
17. Semialgebraic Multilevel for Systems of PDEs
Part VII. Appendices
18. Time-Dependent Parabolic PDEs
19. Nonlinear Equations
References
Index